Sergio Ramos dashed past, the last man out of the Olympic Stadium in Kiev, carrying the Henri Delaunay trophy. A Spain flag was folded up on its top and a medal hung round his neck. "Sorry," he shot with a smile as he passed an Italian friend. Photos. Handshakes. Embraces. More smiles. Everyone wanted a glimpse of the trophy. And yet people were already thinking about another one: the 2014 World Cup. The relentless search for the next challenge, the desire to move the story on before anyone has even digested what just occurred, had begun. It was their job now to slow everyone down, to pause a little, to enjoy it and to comprehend it.

"I'm not sure we're conscious of what we have done yet," Cesc Fábregas said. Others had already wondered if they could do it again. It was ever thus. "Four years ago, when we won the Euros, people asked us to win the World Cup," Iker Casillas said. "When we won the World Cup, they said we had to win the Euros again. I've just left the dressing room here and people are already asking for the World Cup again."

There was a pride in his voice but also a certain exasperation. The problem with always winning is that you must always win. Spain's players denied it but there was a curious sense of obligation about this tournament. Obligation fulfilled, another one was placed before them.

There was something different about the celebrations here. Spain's dressing room was full of kids. Vicente del Bosque's son Alvaro, who has Down's Syndrome and has become almost symbolic of this team, embraced the squad. His father's emotions showed at last. David Villa and Carles Puyol, men who had been so important in 2008 and 2010 but missed Euro 2012 through injury, joined them. Puyol had insisted on paying for his match ticket; the Spanish Federation refused to let him. Both men tried to hang back; Del Bosque refused to let them, dragging them into the heart of the celebrations.

These celebrations were quieter than the previous two, a reflection of expectation and obligation, the moment in which Spain find themselves. "The first title brings the most euphoria, the most emotion, because it comes after so many years [44] of waiting," Gerard Piqué said. "The second brings a little less and the third is a kind of internal satisfaction. And now? Now for the World Cup qualifiers. This happiness gives us the energy to go on fighting and trying to win more things."

Del Bosque had said something similar on the eve of the final. "What will you do on Tuesday?" he was asked. This had after all been a draining month, a difficult one, a month in which, in his own understated way, the Spain coach had felt the need to speak out in defence of his team. And in doing so send a message to his players too. "On Tuesday?" he replied. "Prepare for the World Cup qualifiers."

There was a contradiction there. Del Bosque had previously complained that, while he had witnessed other teams celebrating their passage beyond the group, arms aloft, Spain's players had barely reacted. As if it was nothing. He wanted them, and the rest of us, to appreciate the achievement, to value it. After the final the discourse from the players was similar. Slow down, savour this. Appreciate it. This is historic, whatever comes next. Even if nothing comes next ever again. "The culmination of everything we've done," as Andrés Iniesta put it. "Now, what we have to do is enjoy the moment."

He was right, of course. The trouble with "culmination" is that it sounds like the end and no one here wanted to say that it was the end. Even as they tried to make this moment linger, even as they rebelled against being dragged into more obligation, even as they sought to escape the assumption that this was somehow easy, it was inevitable that they would look ahead. The question was inescapable: can this team keep winning? Can this astonishing, unique run be continued?

The evidence until now suggests that they can. No one really expected them to come this far. No one expects any team to. But beyond the talent this is also an extremely competitive group. "Success normally dimishes hunger," Del Bosque said before the final, "but they have not lost one iota of their competitiveness or humility." There is a quiet determination exhibited by the coach and his players. "Vicente is the embodiment of quiet composure and credibility, the foundation of our success," Piqué said. There is also an identity now, a pathway to follow. Spain's philosophy is not some moral crusade, even if it can feel like it is; it is a means of competing. Tiki taka too is pragmatic.

"Everyone thought that we were finished after the World Cup," Fábregas said. "They thought we might ease up but here we are again. We will try to continue. We believe in what we do and we have been proven right. We can't play long balls. Iniesta is not [physically] strong, I am not strong, Silva is not strong. We have to combine. This is the way we have to play and the way we enjoy playing."

There is one issue. Xavi Hernández has embodied Spain's self-discovery, its identity. He is the ideologue. He is also 32. The next World Cup may be a step too far. "I don't think he will give it up yet," Fábregas said. "[And] there will be a before and after Xavi." His departure will be the end of an era. Yet the After Xavi period no longer looms quite so darkly as it once did; transition can perhaps avoid trauma.

"It looks like some people will go but the new generation are exactly the same," Fábregas continued. "They are humble, they really want to work hard, they believe in our project, the same style, and we're proud of that. We have Jordi Alba and Busquets, me, Piqué, players who are 23 or 25. Iniesta too."

Of Spain's team only three are over 30: Xavi, Casillas and Xabi Alonso. By age, Iniesta has at least two tournaments left in him, Cesc three, Alba four. Del Bosque has quietly carried out a generational renewal already and has laid the foundations for more players to come into the squad over the next two years. The transition has been smooth. The idea and the key personnel have remained the same but there has been a quiet evolution.

Of this squad only 11 were involved in 2008. Spain's second string, players who played few minutes, would surely start for other countries. Eventually they will start for Spain. Juan Mata, Javi Martínez, Fernando Llorente and Pedro got less than an hour between them. Thiago Alcântara, Ander Herrera and Iker Munian did not even get in the squad. Last summer they were European champions at Under-21 level. It is a well-trodden path. ICasillas and Xavi, two emblems of this selección, of the unity and philosophy, won the 1999 World Youth Championships together. "We learnt to win," Casillas said.

The problem is loading Spain's emerging players, or even their already established young players, with responsibility and obligation; assuming it will be easy and leaving a legacy of suffocatingly unrealistic expectation. This is a unique generation and should be judged as such. The next generation, too, must be judged on its own merits. How can it be fairly measured against the most successful international team ever?

"Time goes by for everyone," said Casillas. "As a goalkeeper I can carry on for a bit longer but there are people below us pushing us hard. Us veterans have the responsibility to give way to the players coming through. We have got used to winning from a very young age. We won the Under-16s, the Under-19s, the Under-20s. Almost everyone here has been through those categories. But I tell you something: in a couple of years there will be new players and, although it is true that we have a great Under-21 team, you still have to unite that group and make it work."

There is 'work' and there is repeating this treble. That is a near-impossible task for anyone. That was the point Spain's captain was most keen to get across: this is not normal, even if the criticism, treating a third successive final as if it was not sufficient, made it appear so. "I wouldn't say the criticism was unfair," Casillas said. "But the thing is, this team set the bar so, so high that the second we drop a few centimetres people say we're not the team that we were.What I will say is that I think it is very hard for any Spanish team in the future to do what we have done again. I really hope it happens but it is not easy. I would love to see it."

The raw material may be there, the identity too, and they will certainly try. "It is not easy to keep winning but we have done that," Iniesta said. "Now we have a challenge: to carry on." "This is a unique, unforgettable generation but we can't stop now," Piqué said. "We have to try to keep winning until the day our bodies give up and say: 'no more'. Then we'll retire. And then we'll look back and we'll realise what we have done."